Incorporating spatially variable bottom stress and Coriolis force into 2D, a posteriori, unstructured mesh generation for shallow water models

Abstract

AbstractAn enhanced version of our localized truncation error analysis with complex derivatives (LTEA−CD ) a posteriori approach to computing target element sizes for tidal, shallow water flow, LTEA+CD , is applied to the Western North Atlantic Tidal model domain. The LTEA + CD method utilizes localized truncation error estimates of the shallow water momentum equations and builds upon LTEA and LTEA−CD‐based techniques by including: (1) velocity fields from a nonlinear simulation with complete constituent forcing; (2) spatially variable bottom stress; and (3) Coriolis force. Use of complex derivatives in this case results in a simple truncation error expression, and the ability to compute localized truncation errors using difference equations that employ only seven to eight computational points. The compact difference molecules allow the computation of truncation error estimates and target element sizes throughout the domain, including along the boundary; this fact, along with inclusion of locally variable bottom stress and Coriolis force, constitute significant advancements beyond the capabilities of LTEA. The goal of LTEA + CD is to drive the truncation error to a more uniform, domain‐wide value by adjusting element sizes (we apply LTEA + CD by re‐meshing the entire domain, not by moving nodes). We find that LTEA + CD can produce a mesh that is comprised of fewer nodes and elements than an initial high‐resolution mesh while performing as well as the initial mesh when considering the resynthesized tidal signals (elevations). Copyright © 2008 John Wiley & Sons, Ltd.